Re: Mandy Jane's Corner

Re: Mandy Jane's Corner

The 2 extra questions are:(Q1)Joe is to get £9 for every £3 that Harry gets.The total shared is £600.Give the amounts that Joe and Harry are given.

(Q2)Andrew is given £4 for every £7 that Ian is given.The total shared is £88.

I shall call the most recent one in the thread question (3) it was:(Q3)£480 has to be split so that Jane gets £5 for every £3 that is given to Paul.Calculate how much Paul and Jane get.Work out a total and check that it equals £480

Re: Mandy Jane's Corner

The answers to Q1 and Q2 look correct to me.The answer to Q3 is nearly right in that the £180 figure is right, but the £480 is the original total,so you have multiplied back by 8 when it should have been five.

Re: Mandy Jane's Corner

Re: Mandy Jane's Corner

i can not be on here long as we are off to see some firworks ok could you give me some more on ratio and also give me som on percentages please and i will do them for you and put them on here tomorrow night at around 7.00pm ok

(3)Method:300 / 480 = 0.625180 / 480 = 0.375Answer:So the percentages are 63% and 38% using the convention of roundingupwards if there is a five after the digit being rounded even thoughthe number '0.5' is half way inbetween 0 and 1.Comment:Notice that they do not quite add up to 100%, but this is purely dueto the rounding, apart from that they would add up to 100% in problemswhere you have worked out percentages of a total amount, and have includedall non overlapping components exactly once which add to form the total.

Notes on conventional rounding of numbers:Let us suppose you are rounding to the nearest whole number a numberwhich has digits after the decimal point.The following convention usually applies to numbers between 0 and 1:0.1 rounds down to 00.2 rounds down to 00.3 rounds down to 00.4 rounds down to 00.5 is a borderline case we usually round this up to 10.6 rounds up to 10.7 rounds up to 10.8 rounds up to 10.9 rounds up to 1

Notice that 0.0 can sometimes be used to mean that the accuracy is toone decimal place. Obviously to the nearest whole number it is 0, andindeed it equals 0.Similarly notice that 1.0 can be used to indicate that the accuacy is toone decimal place. Obviously to the nearest whole number it is 1, andit of course equals 1.

Often you will have to give an answer to a certain number of decimal places.For instance: Example 1: Round 1.476 to 2 decimal places.Method: Since the second digit after the decimal point is 7 we look at the nextnumber. It is greater than 5. Therefore rounding up is appropriate.Answer: 1.48

Example 2: Round 4.685 to 2 decimal places.Method: Since the second digit after the decimal point is 8 we look to the nextdigit. It is 5 and by convention an upward rounding occurs.Answer: 4.69

Example 3: Round 3.595 to 2 decimal places.Method: Since the second digit is a 9 care has to be taken because an upwardround of this number will cause an overflow carry since a "10" will resultmeaning that the one higher place value digit to the left must go up by one.As it happens the next digit to the right is 5 so upward rounding occurs byconvention. Therefore a 10 results and "59" becomes "60".Answer: 3.60

A few for you to try:Q1: Round to the nearest whole number 4.7Q2: Round to the nearest whole number 7.5Q3: Round to the nearest whole number 3.2Q4: Round to 2 decimal places 8.469Q5: Round to 2 decimal places 2.755Q6: Round to 2 decimal places 3.933Q7: Round to 2 decimal places 9.695Q8: Round to 2 decimal places 1.005Q9: Round to 2 decimal places 0.999Q10: Round to 2 decimal places -4.867

Note that if you have something like 0.49999999... (recurring) then it is considered the same as 0.5 soit rounds up to 1 not down to zero, so be careful about that exception. Most calculators will spot theseries of nines and round to 0.5 for you if that is the result of a division or similar so you do not usuallyneed to worry. Of course if you just had 0.49 and a finite series of nines then it rounds downward whenrounded to the nearest whole number. A number with many nines at the end that terminates is rare in practice,but with calculators that do not automatically round you could get the recurring 9 happen by something likethe process that I have described here:(This will not work on all calculators. Some will correct the rounding error automatically and others are caught out.)A method to get 0.49999.... is to start with 0.4 in the calculator and then add (1/30) three times.On my calculator it rounds up to 0.5 upon the third addition of 0.033333333.... but has retained a smalldiscrepancy. You can then subtract the 0.5 and then obtain "-1 E-14" in other words -0.00000000000001a very small negative number: minus a hundred trillionth.If you do 1 divide 6 then times 3 and subtract 0.5 then the answer is positive because the rounding at thestage of 1 divided by 6 is an upward round - the recurring digit is 6, so it rounds up to 7. Since 7 times 3is 21 the last digit is 1, which gives the positive extra 1 at the end of the 12 zeros after the five. Then subtractthe 0.5 and you get plus a hundred trillionth ("1 E-14") 0.00000000000001The number of digits will vary according to what calculator is used.Obviously the correct answer to 0.4 + (1/30) + (1/30) + (1/30) - 0.5 is exactly zero.Also the answer to ((1/6) * 3) - 0.5 is also exactly zero.The calculator answer is an example of an inevitable rounding error caused by the limits of accuracy,some calculators will not be caught out by that trick depending on how they have been programmed to work.

Re: Mandy Jane's Corner

Hi steveb & bob buddy happy new year to you both and Sorry I haven't been on here for some time but I have had some things to sort out and now I have done that ok? I would like to get back to doing maths ok hope you will help me out please? Can you send me an email from both of you to let me know what you think about this please? I am going spend 1 hour a day on maths is fun in the evening ok so can you send me a message back on here please like now?

Re: Mandy Jane's Corner

Happy New Year, mandy!

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.''God exists because Mathematics is consistent, and the devil exists because we cannot prove it'I'm not crazy, my mother had me tested.

Re: Mandy Jane's Corner

Hi agnishom mandy here happy new year to you I will be back on here from tomorrow night at around 7.00 pm ok hope you will be able to join us on here sometimes it would be good to hear from you again? Send me a message back please?